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 A099308 Numbers n whose k-th arithmetic derivative is zero for some k. Complement of A099309. 17
 0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 17, 18, 19, 21, 22, 23, 25, 29, 30, 31, 33, 34, 37, 38, 41, 42, 43, 46, 47, 49, 53, 57, 58, 59, 61, 62, 65, 66, 67, 70, 71, 73, 77, 78, 79, 82, 83, 85, 89, 93, 94, 97, 98, 101, 103, 105, 107, 109, 113, 114, 118, 121, 126, 127, 129, 130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The first derivative of 0 and 1 is 0. The second derivative of a prime number is 0. REFERENCES See A003415 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 EXAMPLE 18 is on this list because the first through fifth derivatives are 21, 10, 7, 1, 0 MATHEMATICA dn[0]=0; dn[1]=0; dn[n_]:=Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; d1=Table[dn[n], {n, 40000}]; nLim=200; lst={1}; i=1; While[i<=Length[lst], currN=lst[[i]]; pre=Intersection[Flatten[Position[d1, currN]], Range[nLim]]; pre=Complement[pre, lst]; lst=Join[lst, pre]; i++ ]; Union[lst] CROSSREFS Cf. A003415 (arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero), A099309 (numbers whose k-th arithmetic derivative is nonzero for all k). Sequence in context: A305847 A248565 A065896 * A074235 A325366 A192189 Adjacent sequences:  A099305 A099306 A099307 * A099309 A099310 A099311 KEYWORD nonn AUTHOR T. D. Noe, Oct 12 2004 STATUS approved

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Last modified May 16 12:25 EDT 2021. Contains 343947 sequences. (Running on oeis4.)